I\'ve been wrestling with this for a few days (not literally). I got confused be

Question

I've been wrestling with this for a few days (not literally). I got confused because I read in a book that E = - ? ? where E is the electric field and ? is the scalar potential. However in my notes I had that for a conservative force F = -??. I got confused because electric force and electric field are not the same thing, but I eventually realised that the ? in force is potential energy and not potential as it is with the electric field.

A long time ago I recall someone telling me that you could miss out a factor in scalar potential. Is this right? my reasoning was that because potential and potential energy only differ by a constant factor for example q (charge), and if you were dealing with just scalar potential and not potential energy you could remove this factor?


On the enclosed attatchment, they are showing that the line integral for work on a conservative field can be written as difference in potential. It looks like it should be = -3?d? but they just write = -?d?, have they missed out the factor of 3?

Explanation / Answer

First if a force is conservative we can write it as F=??. Here ? is a generic potential field. It could be related to the electric potential but it does not have to be. For example it could be the gravitational potential. Sometimes the is an additional constant out front F=k??. It the case of the electric potential its the electron charge. However we can pull the constant inside the gradient and the initial statement still holds.

F=k??=?k?=??


has to do with the fact that the force is a derivative of the potential. Therefore you can add a constant ?0 to the potential and the force will remain unchanged.

?(?(x)+?0)=??(x)+??0=??(x)+0

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